@article{MeraTarchanov2017,
  author    = {Mera, Azal Jaafar Musa and Tarchanov, Nikolaj Nikolaevič},
  title     = {The Neumann Problem after Spencer},
  series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University : Matematika i fizika = Mathematics \& physics},
  volume    = {10},
  journal   = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University : Matematika i fizika = Mathematics \& physics},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2017-10-4-474-493},
  pages     = {474 -- 493},
  year      = {2017},
  abstract  = {When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.},
  language  = {en}
}
@unpublished{MeraTarkhanov2016,
  author    = {Mera, Azal and Tarkhanov, Nikolai Nikolaevich},
  title     = {The Neumann problem after Spencer},
  volume    = {5},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-90631},
  pages     = {21},
  year      = {2016},
  abstract  = {When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.},
  language  = {en}
}
@article{MalassTarkhanov2019,
  author    = {Malass, Ihsane and Tarkhanov, Nikolai Nikolaevich},
  title     = {The de Rham Cohomology through Hilbert Space Methods},
  series = {Journal of Siberian Federal University. Mathematics \& physics},
  volume    = {12},
  journal   = {Journal of Siberian Federal University. Mathematics \& physics},
  number    = {4},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnoyarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2019-12-4-455-465},
  pages     = {455 -- 465},
  year      = {2019},
  abstract  = {We discuss canonical representations of the de Rham cohomology on a compact manifold with boundary. They are obtained by minimising the energy integral in a Hilbert space of differential forms that belong along with the exterior derivative to the domain of the adjoint operator. The corresponding Euler-Lagrange equations reduce to an elliptic boundary value problem on the manifold, which is usually referred to as the Neumann problem after Spencer.},
  language  = {en}
}
@unpublished{Tarkhanov2004,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Harmonic integrals on domains with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26800},
  year      = {2004},
  abstract  = {We study the Neumann problem for the de Rham complex in a bounded domain of Rn with singularities on the boundary. The singularities may be general enough, varying from Lipschitz domains to domains with cuspidal edges on the boundary. Following Lopatinskii we reduce the Neumann problem to a singular integral equation of the boundary. The Fredholm solvability of this equation is then equivalent to the Fredholm property of the Neumann problem in suitable function spaces. The boundary integral equation is explicitly written and may be treated in diverse methods. This way we obtain, in particular, asymptotic expansions of harmonic forms near singularities of the boundary.},
  language  = {en}
}
@article{MalassTarkhanov2020,
  author    = {Malass, Ihsane and Tarkhanov, Nikolaj Nikolaevič},
  title     = {A perturbation of the de Rham complex},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {13},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {5},
  publisher = {Siberian Federal University},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-5-519-532},
  pages     = {519 -- 532},
  year      = {2020},
  abstract  = {We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.},
  language  = {en}
}
@article{HinzSchwarz2022,
  author    = {Hinz, Michael and Schwarz, Michael},
  title     = {A note on Neumann problems on graphs},
  series = {Positivity},
  volume    = {26},
  journal   = {Positivity},
  number    = {4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1385-1292},
  doi       = {10.1007/s11117-022-00930-0},
  pages     = {23},
  year      = {2022},
  abstract  = {We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.},
  language  = {en}
}